Everything Maths Grade 11

10.3 CHAPTER 10. MATHEMATICAL MODELS

Extension: Simulations

A simulation is an attempt to model a real-life situation on a computer so that it can be stud-

ied to see how the system works. By changing variables, predictions may be made about the

behaviour of the system. Simulation is used in many contexts, includingthe modelling of nat-

ural systems or humansystems in order to gaininsight into their functioning. Other contexts

include simulation of technology for performance optimisation, safetyengineering, testing,

training and education.Simulation can be usedto show the eventual real effects of alternative

conditions and coursesof action.

Simulation in education Simulations in education are somewhat like training simulations. They

focus on specific tasks. In the past, video has been used for teachers andeducation students to

observe, problem solveand role play; however,a more recent use of simulations in education

is that of animated narrative vignettes (ANV). ANVs are cartoon-like video narratives of hypo-

thetical and reality-based stories involving classroom teaching and learning. ANVs have been

used to assess knowledge, problem solving skills and dispositions of children and pre-service

and in-service teachers.

Chapter 10 End of Chapter Exercises

1. When an object is dropped or thrown downward, the distance, d, that it falls in time,
   t, is described by the following equation:

s = 5t^2 + v 0 t

In this equation, v 0 is the initial velocity, in m· s−^1. Distance is measured in meters

and time is measured inseconds. Use the equation to find how long it takes a tennis

ball to reach the groundif it is thrown downwardfrom a hot-air balloon that is 500 m

high. The tennis ball is thrown at an initial velocity of 5 m· s−^1.

2. The table below liststhe times that Sheila takes to walk the given distances.
   Time (minutes) 5 10 15 20 25 30
   Distance (km) 1 2 3 4 5 6

Plot the points.

If the relationship between the distances and times is linear, find the equation of the

straight line, using anytwo points. Then use the equation to answer the following

questions:

(a) How long will it takeSheila to walk 21 km?

(b) How far will Sheilawalk in 7 minutes?

If Sheila were to walk half as fast as she is currently walking, what would the graph

of her distances and times look like?

3. The power P (in watts) supplied toa circuit by a 12 volt battery is given by the
   formula P = 12I− 0 , 5 I^2 where I is the current in amperes.
   (a) Since both power and current must be greater than 0 , find the limits of the current
   that can be drawn by the circuit.
   (b) Draw a graph of P = 12I− 0 , 5 I^2 and use your answer tothe first question, to
   define the extent of thegraph.
   (c) What is the maximum current that can be drawn?